Norm-conserving finite-difference beam-propagation method for TM wave analysis in step-index optical waveguides

Abstract

Abstract-Nonconservation

Application of modified finite-difference formulas to the analysis of z-variant rib waveguides

“…Although the present analysis does not ensure second-order accuracy for the tangential component , the first-order term has a much smaller effect than the error caused by a staircase approximation [13]. This leads to a significant improvement in accuracy even for .…”

A Modified Semivectorial BPM Retaining the Effects of the Longitudinal Field Component and Its Application to the Design of a Spot-Size Converter

“…Note that the necessity of the term in (4) (corresponding to the term #A in (7)) has already been pointed out in [1] and [2]. To evaluate the component of the last term in (4), we employ the relation .…”

“…To evaluate the second derivative with respect to the transverse direction, we employ the second-order finite-difference scheme [2], which takes into account the boundary condition at the dielectric interface. The terms #A and #B in (7) are evaluated using the following formula [16]: (8) where indicates the position along the -direction.…”

“…The difficulty becomes significant particularly when a waveguide with an asymmetrical index profile is treated. To resolve this problem, some attempts were made, but most of the previous works neglected the existence of the longitudinal field components [2]- [4], except for the full vectorial treatment done by Montanari et al [5]. In this paper, we newly formulate a semivectorial BPM partially retaining the effects of the longitudinal field component [6].…”

Transverse-Magnetic BPM Analysis of a Step-Index Slab Waveguide Expressed by a Sigmoid Function

“…It should be noted, however, that the transformation technique does not work well for a step-index waveguide. The authors, therefore, numerically investigated the effects of including the variation of the refractive index in detail [4]. On the other hand, Ho and Lu [5] introduced a single scatter approximation for the wide-angle TM wave.…”